Solve -3(4x^{6})^2-3x^4*2x^5(-3x^3)

$$- 3 ( 4 x ^ { 6 } ) ^ { 2 } - 3 x ^ { 4 } \cdot 2 x ^ { 5 } ( - 3 x ^ { 3 } )$$

Evaluate

$$-30x^{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$-3\times \left(4x^{6}\right)^{2}-3x^{9}\times 2\left(-3\right)x^{3}$$

To multiply powers of the same base, add their exponents. Add 9 and 3 to get 12.

$$-3\times \left(4x^{6}\right)^{2}-3x^{12}\times 2\left(-3\right)$$

Expand \left(4x^{6}\right)^{2}.

$$-3\times 4^{2}\left(x^{6}\right)^{2}-3x^{12}\times 2\left(-3\right)$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$-3\times 4^{2}x^{12}-3x^{12}\times 2\left(-3\right)$$

Calculate 4 to the power of 2 and get 16.

$$-3\times 16x^{12}-3x^{12}\times 2\left(-3\right)$$

Multiply -3 and 16 to get -48.

$$-48x^{12}-3x^{12}\times 2\left(-3\right)$$

Multiply 3 and 2 to get 6.

$$-48x^{12}-6x^{12}\left(-3\right)$$

Multiply 6 and -3 to get -18.

$$-48x^{12}-\left(-18x^{12}\right)$$

The opposite of -18x^{12} is 18x^{12}.

$$-48x^{12}+18x^{12}$$

Combine -48x^{12} and 18x^{12} to get -30x^{12}.

$$-30x^{12}$$

Expand

$$-30x^{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$-3\times \left(4x^{6}\right)^{2}-3x^{9}\times 2\left(-3\right)x^{3}$$

To multiply powers of the same base, add their exponents. Add 9 and 3 to get 12.

$$-3\times \left(4x^{6}\right)^{2}-3x^{12}\times 2\left(-3\right)$$

Expand \left(4x^{6}\right)^{2}.

$$-3\times 4^{2}\left(x^{6}\right)^{2}-3x^{12}\times 2\left(-3\right)$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$-3\times 4^{2}x^{12}-3x^{12}\times 2\left(-3\right)$$

Calculate 4 to the power of 2 and get 16.

$$-3\times 16x^{12}-3x^{12}\times 2\left(-3\right)$$

Multiply -3 and 16 to get -48.

$$-48x^{12}-3x^{12}\times 2\left(-3\right)$$

Multiply 3 and 2 to get 6.

$$-48x^{12}-6x^{12}\left(-3\right)$$

Multiply 6 and -3 to get -18.

$$-48x^{12}-\left(-18x^{12}\right)$$

The opposite of -18x^{12} is 18x^{12}.

$$-48x^{12}+18x^{12}$$

Combine -48x^{12} and 18x^{12} to get -30x^{12}.

$$-30x^{12}$$